Simplify x square root of 6x-5 square root of 96x^3

$x \sqrt{6 x} - 5 \sqrt{96 x^{3}}$

Step 1

Simplify each term.

Rewrite $96 x^{3}$ as ${(4 x)}^{2} \cdot (6 x)$ .

Factor $16$ out of $96$ .

$x \sqrt{6 x} - 5 \sqrt{16 (6) x^{3}}$

Rewrite $16$ as $4^{2}$ .

$x \sqrt{6 x} - 5 \sqrt{4^{2} \cdot 6 x^{3}}$

Factor out $x^{2}$ .

$x \sqrt{6 x} - 5 \sqrt{4^{2} \cdot 6 (x^{2} x)}$

Move $6$ .

$x \sqrt{6 x} - 5 \sqrt{4^{2} x^{2} \cdot 6 x}$

Rewrite $4^{2} x^{2}$ as ${(4 x)}^{2}$ .

$x \sqrt{6 x} - 5 \sqrt{{(4 x)}^{2} \cdot 6 x}$

Add parentheses.

$x \sqrt{6 x} - 5 \sqrt{{(4 x)}^{2} \cdot (6 x)}$

$x \sqrt{6 x} - 5 \sqrt{{(4 x)}^{2} \cdot (6 x)}$

Pull terms out from under the radical.

$x \sqrt{6 x} - 5 (4 x \sqrt{6 x})$

Multiply $4$ by $- 5$ .

$x \sqrt{6 x} - 20 x \sqrt{6 x}$

$x \sqrt{6 x} - 20 x \sqrt{6 x}$

Step 2

Subtract $20 x \sqrt{6 x}$ from $x \sqrt{6 x}$ .

$- 19 x \sqrt{6 x}$

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